1. Tardigrade
  2. Question
  3. Mathematics
  4. By Simpson rule taking n=4, the value of the integral ∫01 (1/1+x2) d x is equal to

Q. By Simpson rule taking $n=4$, the value of the integral $\int_{0}^{1} \frac{1}{1+x^{2}} d x$ is equal to

MHT CETMHT CET 2011 Report Error

Solution:

Here, $h=1 / 4,=0.25, y=\frac{1}{1+x^{2}}$
x y
1 0 1.0
2 0.25 0.941
3 0.5 0.8
4 0.75 0.64
5 1 0.5

By Simpson's Rule
$\int_\limits{0}^{1} \frac{d x}{1+x^{2}}=\frac{1}{4 \times 3}$
$[(1+0.5) + 4(0.941+ 0.64)+2(0.8)]$
$=\frac{1}{12}[9,424]=0.785$

Questions from MHT CET 2011

1. The inverse of the proposition $ \left(p \wedge \sim q\right) \Rightarrow r $ is

2. In a Boolean Algebra $ B $ , for all $ x $ , $ y $ in $ B $ , $ x \wedge \left(x \vee y\right) $ is equal to

3. For the circuit show below, the Boolean polynomial is

4. The value of $ \left(1+\Delta\right) \left(1- \nabla\right) $ is

5. The multiplicative inverse of $ A = \begin{bmatrix}cos\,\theta&-sin\,\theta \\ sin\,\theta &cos\,\theta \end{bmatrix} $ is

Mathematics Most Viewed Questions

1. The solution of $\frac{dy}{dx} = \frac{y}{x}+\tan \frac{y}{x}$ is

WBJEE 2011 Differential Equations

2. The solution of the differential equation $\frac{dy}{dx} = (x +y)^2$ is

COMEDK 2009 Differential Equations

3. $\int\frac{1}{\sin x\, \cos x}$ dx is equal to

KEAM 2016 Integrals

4. If $\begin{bmatrix}1&- \tan\theta \\ \tan \theta&1\end{bmatrix}\begin{bmatrix}1&\tan \theta \\ - \tan \theta &1\end{bmatrix}^{-1} = \begin{bmatrix}a&-b\\ b&a\end{bmatrix}$ then

COMEDK 2009 Matrices

5. The value of $ \int{\frac{{{x}^{2}}+1}{{{x}^{4}}-{{x}^{2}}+1}}dx $ is

KEAM 2007 Integrals

Latest Updates